By Mattias Nordin, Per Bodin, Per-Olof Gutman (auth.), Gang Tao PhD, Frank L. Lewis PhD (eds.)
A entire connection with adaptive keep watch over of platforms with nonsmooth nonlinearities such as:
• part failure;
• time delays.
These nonlinearities in business actuators reason critical difficulties within the movement keep watch over of business strategies, really in view of contemporary specifications for velocity and precision of circulation, reminiscent of take place in semiconductor production, precision machining and in different places. Actuator nonlinearities are ubiquitous in engineering perform and restrict keep watch over method performance.
While regular suggestions keep an eye on on my own can't deal with those nonsmooth nonlinearities successfully, this ebook, with unified and systematic adaptive layout equipment constructed in sixteen chapters, indicates how such nonlinear features should be successfully compensated for through the use of adaptive and clever regulate options. this enables wanted procedure functionality to be accomplished within the presence of doubtful nonlinearities.
With broad surveys of literature and accomplished summaries of varied layout equipment the authors of the e-book chapters, who're specialists of their parts of curiosity, current new options to a few vital concerns in adaptive keep watch over of structures with a variety of forms of nonsmooth nonlinearities.
In addition to offering recommendations, the publication is usually aimed toward motivating extra examine actions within the very important box of adaptive keep watch over of nonsmooth nonlinear commercial platforms through formulating numerous not easy open difficulties in similar areas.
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Extra resources for Adaptive Control of Nonsmooth Dynamic Systems
G. Brandenburg. Stability of a speed controlled elastic two-mass system with backlash and Coulomb friction and optimization by a load observer. In Symposium: Modelling and Simulation tor Control 0/ Lumped and Distributed Parameter Systems, pages 107~113, Lilie, 1986. IMACS-IFACS. 4. G. Brandenburg, H. Hertie, and K. Zeiselmair. Dynamic influence and partial compensation of coulomb friction in a position- and speed-controlled elastic two-mass systems. In IFAC World Congress, Munieh, 1987. 30 Mattias Nordin, Per Bodin and Per-Olof Gutman 5.
0) 2: br . The verification for m;(t) 2: ml and b;(t) 2: bl is symmetrie. The proofis shown by contradictions. First, notice t~at at a finite time t, v(t) is finite because IUd(t)1 ~ ße<>:t. (t) are continuous at time t. (t) < br for some t 2: o. (t) have to cross m r and/or br at some time tl. More precisely, there exists some time tl 2: 0 and some sufficiently small positive constant 8 2: 0 such that one of the following scenarios occurs, 1. (tl 2. W. Bai 3. 1t < 8 We will show contradictions in each case.
A modification of the dead zone model that does not violate Lemma 1 is given by (27) An interpretation of (27) is that there is always right contact for (Od, Bd) E A+ with T = k(Od - 0:) + cB d and always left contact for (Od, Bd) E A_ with T = k(Od) + 0:) + CBd' Compare equations (6)-(8), (23) and Figures 2a and 2b. Remark 2. Note that if k/c -+ 00 the solution of (13) immediately goes to Od = Ob so now approximation (ii) in Remark 1 made for the phase plane model is exact, namely Os(tl) = O. Furthermore the slope of the left respectively right border of Al respectively A2 goes to -00, and hence the areas Al and A2 to zero, so the phase plane model converges to the classical dead zone model (24), to which the dead zone models (26) and (27) also converge.